A Cauchy problem for the asymmetric Parabolic equation in polar coordinates with the perturbed diffusivity

Tóm tắt

The inverse problem for the heat equation plays an important area of study and application. Up to now, the backward heat problem (BHP) in Cartesian coordinates has been arisen in many articles, but the BHP in different domains such as polar coordinates, cylindrical one or spherical one is rarely considered. This paper’s purpose is to investigate the BHP on a disk, especially, the problem is associated with the perturbed diffusivity and the space-dependent heat source. In order to solve the problem, the authors apply the separation of variables method, associated with the Bessel’s equation and Bessel’s expansion. Based on the exact solution, the regularized solution is constructed by using the modified quasi-boundary value method. As a result, a Holder type of convergence rate has been obtained. In addition, a numerical experiment is given to illustrate the flexibility and effectiveness of the used method.